How Do You Calculate Capacitance in a Series RC Circuit?

In summary: Yes. Solve for C.In summary, the conversation discusses a series RC circuit with a known resistance and unknown capacitance, driven by an alternating electromotive force and with a given frequency and current. The equations (1) and (2) are attempted to be used to calculate the capacitance, but are found to be incorrect. The correct equation is derived to be sqrt( R^2 + (1/2(pi)fC)^2), and then solved for C.
  • #1
SereneKi
12
0

Homework Statement



Consider a series RC circuit with R = 151 Ω and an unknown capacitor C as shown below.


http://www.flickr.com/photos/67342906@N0…


The circuit is driven by an alternating electromotive force with εRMS = 174 V at a frequency of f = 7.70 Hz. The current in the circuit is IRMS = 0.310 A. Calculate the capacitance C.

Homework Equations



(1) I(rms)=V(source) / ( R+ (1/C))
(2) I(rms)=C x V(source) / ( 1+ RC)

The Attempt at a Solution



tried to plug them into equation (1) to get C but it didn't work

0.31 =174 / (151+ 1/C )

C=0.00244 F
 
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  • #3
SereneKi said:

Homework Statement



Consider a series RC circuit with R = 151 Ω and an unknown capacitor C as shown below.


http://www.flickr.com/photos/67342906@N0…


The circuit is driven by an alternating electromotive force with εRMS = 174 V at a frequency of f = 7.70 Hz. The current in the circuit is IRMS = 0.310 A. Calculate the capacitance C.

Homework Equations



(1) I(rms)=V(source) / ( R+ (1/C))
(2) I(rms)=C x V(source) / ( 1+ RC)

The Attempt at a Solution



tried to plug them into equation (1) to get C but it didn't work

0.31 =174 / (151+ 1/C )

C=0.00244 F

Your Relevant Equations are not correct in that they are not handling the summation of resistance (of the resistor) and reactance (of the capacitor) properly; they should add in quadrature (square root of sum of squares, just like vector components). Also, the reactance should depend upon the frequency of the driving signal, which in this case is given as 7.70 Hz.
 
Last edited by a moderator:
  • #4
gneill said:
Your Relevant Equations are not correct in that they are not handling the summation of resistance (of the resistor) and reactance (of the capacitor) properly; they should add in quadrature (square root of sum of squares, just like vector components). Also, the reactance should depend upon the frequency of the driving signal, which in this case is given as 7.70 Hz.

So

Irms = sqrt( R^2 + (1/2(pi)fC)^2)
 
  • #5
SereneKi said:
So

Irms = sqrt( R^2 + (1/2(pi)fC)^2)

Now you're missing the electric potential :smile: Remember you're writing Ohm's law, so I = E/Z, where here Z is the sum of resistance and reactance as you've calculated above.
 
  • #6
gneill said:
Now you're missing the electric potential :smile: Remember you're writing Ohm's law, so I = E/Z, where here Z is the sum of resistance and reactance as you've calculated above.

So

Erms/Irms = sqrt( R^2 + (1/2(pi)fC)^2)
 
  • #7
SereneKi said:
So

Erms/Irms = sqrt( R^2 + (1/2(pi)fC)^2)

Yes. Solve for C.
 

FAQ: How Do You Calculate Capacitance in a Series RC Circuit?

What is capacitance and how is it measured?

Capacitance is the ability of a system to store electric charge. It is measured in units of farads (F) and is represented by the symbol C. Capacitance can be measured using a device called a capacitor, which consists of two conductive plates separated by an insulating material. The capacitance of a capacitor is determined by the size of the plates, the distance between them, and the type of insulating material used.

What is an RC circuit and how does it work?

An RC circuit is a circuit that contains both a resistor (R) and a capacitor (C). These two components work together to control the flow of electric current in the circuit. The resistor limits the flow of current, while the capacitor stores and releases charge. When the circuit is first connected, the capacitor charges up to the same voltage as the power source. As the capacitor discharges, the voltage across it decreases and the current decreases.

How is the time constant of an RC circuit calculated?

The time constant of an RC circuit is determined by the product of the resistance (R) and the capacitance (C) in the circuit. It is calculated using the formula τ = RC, where τ is the time constant in seconds. The time constant represents the amount of time it takes for the capacitor to charge up to approximately 63% of its maximum charge or discharge to approximately 37% of its initial charge.

How does capacitance affect the behavior of an RC circuit?

The capacitance in an RC circuit affects the rate at which the capacitor charges and discharges. A larger capacitance will result in a longer time constant and a slower rate of charge/discharge. This means that the capacitor will take longer to reach its maximum charge and will take longer to discharge. A smaller capacitance will result in a shorter time constant and a faster rate of charge/discharge.

What is the purpose of an RC circuit in electronic devices?

RC circuits are commonly used in electronic devices for a variety of purposes. They can be used to filter out unwanted signals, stabilize voltage levels, and control the timing of circuits. They are also commonly used in power supplies to smooth out fluctuations in the electricity supply. Additionally, RC circuits are used in timing circuits for things like flashing lights or generating sound in electronic devices.

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